If vector a=< 1, –1, 0 > and vector b=< 0, –1, 2 > are vectors a and b orthogonal, parallel, or neither? Provide

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: Find the length of the vector.v = (4, 3)

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Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Are the following vectors linearly independent? Yes No , ,,

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Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: Show that if u and v are orthogonal unit vectors then u x v is also a unit vector.

A: To show: That if u and v are orthogonal unit vector, then prove that u×v is also a unit vector:…

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Given a position vector v, why are there infinitely many vectors equal to v?

A: For given position vector, there are infinitely many translations possible. It is known that the…

Q: Is it true that if vectors a-b and a+b are orthogonal, then |a|=|b|.

A: For orthogonal, dot product of two vector is zero

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: A vector is in standard position if the _____ of the vector is placed at the ______ ofa rectangular…

A: To fill up the blanks,  A vector is in standard position if the _____ of the vector is placed at the…

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

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Q: Draw an example of two opposite vectors that are not parallel or explain why such vectors don't…

A: To find: Two vectors opposite in direction which are not parallel. or, Explain why above two vectors…

Q: 2. Find two unit vectors orthogonal to both and .

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Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

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Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: own your onw word, meaning for two vectors to be parallel?

A: Vectors are parallel if they have the same direction Both components of one vector must be in the…

Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

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Q: Two nonzero vectors are perpendicular if and only if their _____ _______ is equal to______.

A: Given:Two nonzero vectors are perpendicular if and only if their ______is equal to ______

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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Q: If vector A is any non-zero vector, a unit vector in the same direction of A would be?

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Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: Find the magnitude of the vector AB A=(-2,3) and B=(3, - 4)

A: A vector has both magnitude and direction. The direction of a vector is indicated by an arrow.…

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: If vector a= and vector b= .. are vectors a and b orthogonal, parallel, or neither? Provide…

A: Topic = Vector   2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Will this statement be true or false and why? The vector u results when a vector u – v is added to…

A: topic - true

Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1